Finite Group Databasebeta

← #11787619

Subgroups — #11787619

Order 1152.

465 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#568C211yesmaximal, characteristic, complemented
2#10589925C211yesmaximal, characteristic
3#10588917C211yesmaximal, characteristic, complemented
4#10588819C211yesmaximal, characteristic, complemented
5#10588811C211yesmaximal, characteristic, complemented
6#10588236C211yesmaximal, characteristic, complemented
7#10588231C211yesmaximal, characteristic, complemented
8#72020—31nomaximal
9C2×C9×#41C2211yescharacteristic
10C2×#3697C2211yescharacteristic
11C9×#131—22no—
12C9×#131—22no—
13C2×C9×M16—22no—
14C2×C9×M16C2211yescharacteristic
15C2×C9×M16C2211yescharacteristic
16#63513—22no—
17#63512C412yescomplemented
18#63511C412yescomplemented
19#63505—21no—
20#63495—21no—
21#63488C2211yescharacteristic
22C2×#3667C2211yescharacteristic
23C22×C9⋊C8C2211yescharacteristic
24#63395—21no—
25#63392—21no—
26#63384—22no—
27(C2×D9)⋊C8—22no—
28C3×#568D311yescharacteristic
29#5822—31no—
30#5233—31no—
31#5139—31no—
32#5129—31no—
33#4558—31no—
34#4556—31no—
35C9×#41—21no—
36C9×#41—21no—
37C9×#41C2×C412yes—
38C9×#41D412yes—
39C2×Q8×C9D411yescharacteristic
40C2×D4×C9—21no—
41C2×D4×C9D411yescharacteristic
42C22×C4×C9—21no—
43C22×C4×C9C2311yescharacteristic
44C2×#611—21no—
45#3697—21no—
46#3697—21no—
47#3697—21no—
48#3697—21no—
49C2×D36C2×C411yescharacteristic
50C2×C4×D9—21no—
51C2×Dic18C2×C411yescharacteristic
52C9×M16—24no—
53C9×M16—21no—
54C9×M16—21no—
55C9×M16—21no—
56C9×M16D412yes—
57C2×C8×C9—24no—
58C2×C8×C9—21no—
59C2×C8×C9D412yes—
60#3676—21no—
61#3675—22no—
62#3674—22no—
63#3673—22no—
64#3672—22no—
65C4⋊Dic9—21no—
66C4×Dic9—21no—
67#3667—21no—
68#3667C2×C412yes—
69C2×C9⋊C8—21no—
70C2×C9⋊C8—21no—
71C2×C9⋊C8—21no—
72C2×C9⋊C8—21no—
73#1881—91noSylow
74C2×C3×#41C2×D311yescharacteristic
75C2×#235—31no—
76C3×#131—22no—
77C3×#131—22no—
78C2×C3×M16—22no—
79C2×C3×M16C2×D311yescharacteristic
80C2×C3×M16C2×D311yescharacteristic
81#951—32no—
82#950—62no—
83#949—32no—
84#942—61no—
85#932—61no—
86#926—31no—
87C2×#208—31no—
88C22×C3⋊C8—31no—
89#835—61no—
90#832—61no—
91#825—62no—
92(C2×D3)⋊C8—62no—
93C23×C9—21no—
94C23×C9#4111yescharacteristic
95C22×D9—21no—
96Q8×C9—21no—
97Q8×C9C22⋊C412yes—
98D4×C9—22no—
99D4×C9—22no—
100D4×C9—21no—
101D4×C9C22⋊C412yes—
102C2×C4×C9—21no—
103C2×C4×C9—22no—
104C2×C4×C9—22no—
105C2×C4×C9C22×C411yescharacteristic
106C2×C4×C9C2×D411yescharacteristic
107C2×C4×C9C2×D411yescharacteristic
108C2×C4×C9C2×D411yescharacteristic
109C2×C4×C9C2×D411yescharacteristic
110C2×C4×C9#4111yescharacteristic
111#611—41no—
112#611—41no—
113C2×Dic9—21no—
114C2×Dic9—41no—
115D36—21no—
116D36—21no—
117C4×D9—41no—
118C4×D9—41no—
119Dic18—21no—
120Dic18—21no—
121C8×C9—22no—
122C8×C9—22no—
123C9⋊C8—22no—
124C9⋊C8—41no—
125#575—91no—
126#568D911yescharacteristic, complemented
127#421—91no—
128#416—91no—
129#408—91no—
130#344—91no—
131#341—91no—
132C3×#41—21no—
133C3×#41—21no—
134C3×#41C4×D312yes—
135C3×#41#6712yes—
136C2×C3×Q8D1211yescharacteristic
137C2×C3×D4—21no—
138C2×C3×D4D1211yescharacteristic
139C22×C3×C4—21no—
140C22×C3×C4C22×D311yescharacteristic
141C2×#67—61no—
142#235—61no—
143#235—61no—
144#235—61no—
145#235—61no—
146C2×D12—31no—
147C2×C4×D3—61no—
148C2×Dic6—31no—
149C3×M16—24no—
150C3×M16—21no—
151C3×M16—21no—
152C3×M16—21no—
153C3×M16#6712yes—
154C2×C3×C8—24no—
155C2×C3×C8—21no—
156C2×C3×C8#6712yes—
157#217—61no—
158#216—62no—
159#215—62no—
160#214—62no—
161#213—62no—
162C4⋊Dic3—61no—
163C4×Dic3—61no—
164#208—32no—
165#208—61no—
166C2×C3⋊C8—61no—
167C2×C3⋊C8—61no—
168C2×C3⋊C8—61no—
169C2×C3⋊C8—61no—
170C22×C9—22no—
171C22×C9—41no—
172C22×C9—81no—
173C22×C9C4×D411yescharacteristic
174C22×C9#12111yescharacteristic
175C22×C9#12311yescharacteristic
176C2×D9—42no—
177C2×D9—41no—
178C4×C9—22no—
179C4×C9C2×C22⋊C411yescharacteristic
180C4×C9C4×D411yescharacteristic
181C4×C9#12011yescharacteristic
182C4×C9#12111yescharacteristic
183Dic9—41no—
184Dic9—81no—
185C2×#41—91no—
186C2×#41C2×D911yescharacteristic
187#137—92no—
188#137—181no—
189AGL(1,ℤ/8)—92no—
190AGL(1,ℤ/8)—181no—
191#135—182no—
192#131—22no—
193#131—22no—
194C2×M16—22no—
195C2×M16—91no—
196C2×M16C2×D911yescharacteristic
197C2×M16C2×D911yescharacteristic
198C22×C8—91no—
199#117—91no—
200#104—182no—
201#103—181no—
202#102—181no—
203C22⋊C8—182no—
204C23×C3—21no—
205C23×C3#23511yescharacteristic
206C22×D3—61no—
207C3×Q8—21no—
208C3×Q8(C2×D3)⋊C412yes—
209C3×D4—22no—
210C3×D4—22no—
211C3×D4—21no—
212C3×D4(C2×D3)⋊C412yes—
213C2×C3×C4—21no—
214C2×C3×C4—22no—
215C2×C3×C4—22no—
216C2×C3×C4C2×C4×D311yescharacteristic
217C2×C3×C4C2×D1211yescharacteristic
218C2×C3×C4#23511yescharacteristic
219C2×C3×C4C2×#6711yescharacteristic
220C2×C3×C4C2×#6711yescharacteristic
221C2×C3×C4C2×#6711yescharacteristic
222#67—121no—
223#67—121no—
224C2×Dic3—61no—
225C2×Dic3—121no—
226D12—61no—
227D12—61no—
228C4×D3—121no—
229C4×D3—121no—
230Dic6—61no—
231Dic6—61no—
232C3×C8—22no—
233C3×C8—22no—
234C3⋊C8—62no—
235C3⋊C8—121no—
236C2×C9—21no—
237C2×C9—21no—
238C2×C9—21no—
239C2×C9—42no—
240C2×C9#38611yescharacteristic
241D9—81no—
242#41—21no—
243#41—21no—
244#41—181no—
245#41—181no—
246#41—181no—
247#41—181no—
248#41C4×D912yes—
249#41#61112yes—
250C2×Q8—91no—
251C2×Q8D3611yescharacteristic
252C2×D4—21no—
253C2×D4—91no—
254C2×D4—181no—
255C2×D4D3611yescharacteristic
256C22×C4—21no—
257C22×C4—181no—
258C22×C4C22×D911yescharacteristic
259Q16—182no—
260SD16—182no—
261SD16—182no—
262D8—182no—
263M16—24no—
264M16—21no—
265M16—21no—
266M16—21no—
267M16—92no—
268M16—181no—
269M16#61112yes—
270C2×C8—24no—
271C2×C8—21no—
272C2×C8—181no—
273C2×C8—181no—
274C2×C8—181no—
275C2×C8—181no—
276C2×C8#61112yes—
277C4⋊C4—181no—
278C22⋊C4—181no—
279C42—181no—
280C22×C3—22no—
281C22×C3—41no—
282C22×C3—81no—
283C22×C3C4×#6711yescharacteristic
284C22×C3#92911yescharacteristic
285C22×C3#93011yescharacteristic
286C2×D3—122no—
287C2×D3—121no—
288C3×C4—22no—
289C3×C4C2×(C2×D3)⋊C411yescharacteristic
290C3×C4C4×#6711yescharacteristic
291C3×C4#93011yescharacteristic
292C3×C4#95311yescharacteristic
293Dic3—121no—
294Dic3—241no—
295C9#188111yescharacteristic, complemented, Sylow
296C23—21no—
297C23—181no—
298C23#369711yescharacteristic
299Q8—21no—
300Q8—181no—
301Q8—181no—
302Q8(C2×D9)⋊C412yes—
303D4—22no—
304D4—22no—
305D4—21no—
306D4—181no—
307D4—181no—
308D4—361no—
309D4—361no—
310D4(C2×D9)⋊C412yes—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—181no—
315C2×C4—361no—
316C2×C4—361no—
317C2×C4—361no—
318C2×C4C2×C4×D911yescharacteristic
319C2×C4C2×D3611yescharacteristic
320C2×C4#369711yescharacteristic
321C2×C4C2×#61111yescharacteristic
322C2×C4C2×#61111yescharacteristic
323C2×C4C2×#61111yescharacteristic
324C8—22no—
325C8—22no—
326C8—182no—
327C8—361no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—42no—
332C2×C3#521311yescharacteristic
333D3—241no—
334C22—22no—
335C22—41no—
336C22—81no—
337C22—362no—
338C22—361no—
339C22C4×#61111yescharacteristic
340C22#6349111yescharacteristic
341C22#6349211yescharacteristic
342C4—22no—
343C4—361no—
344C4—721no—
345C4C2×(C2×D9)⋊C411yescharacteristic
346C4C4×#61111yescharacteristic
347C4#6349211yescharacteristic
348C4#6351511yescharacteristic
349C3#7202011yescharacteristic
350C2—21no—
351C2—21no—
352C2—21no—
353C2—42no—
354C2—721no—
355C2#1058889311yescharacteristic
subgroupG/H
centerC4#63515
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#568C2
socleC2×C3#5213
prime radical#10589925C2
cosocleC22×C4×C9C23
hypercenter#568D9
hypocenterC9#1881
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C9×#568C2semidirect
3. #10588917C2semidirect
4. #10588819C2semidirect
5. #10588811C2semidirect
6. #10588236C2semidirect
7. #10588231C2semidirect
17. #63512C4semidirect
18. #63511C4semidirect
126. #568D9semidirect
295. C9#1881semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C9×#5682
#105899252
#105889172
#105888192
#105888112
#105882362
#105882312
#720203